{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T12:45:26Z","timestamp":1768567526588,"version":"3.49.0"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,13]],"date-time":"2023-01-13T00:00:00Z","timestamp":1673568000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["U2030205"],"award-info":[{"award-number":["U2030205"]}]},{"name":"National Natural Science Foundation of China","award":["62003075"],"award-info":[{"award-number":["62003075"]}]},{"name":"National Natural Science Foundation of China","award":["61903065"],"award-info":[{"award-number":["61903065"]}]},{"name":"National Natural Science Foundation of China","award":["62003074"],"award-info":[{"award-number":["62003074"]}]},{"name":"National Natural Science Foundation of China","award":["2022JDJQ0040"],"award-info":[{"award-number":["2022JDJQ0040"]}]},{"name":"Sichuan Science and Technology Planning Project","award":["U2030205"],"award-info":[{"award-number":["U2030205"]}]},{"name":"Sichuan Science and Technology Planning Project","award":["62003075"],"award-info":[{"award-number":["62003075"]}]},{"name":"Sichuan Science and Technology Planning Project","award":["61903065"],"award-info":[{"award-number":["61903065"]}]},{"name":"Sichuan Science and Technology Planning Project","award":["62003074"],"award-info":[{"award-number":["62003074"]}]},{"name":"Sichuan Science and Technology Planning Project","award":["2022JDJQ0040"],"award-info":[{"award-number":["2022JDJQ0040"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Magnetic Flux Leakage (MFL) visualization technique is widely used in the surface defect inspection of ferromagnetic materials. However, the information of the images detected through the MFL method is incomplete when the defect (especially for the cracks) is complex, and some information would be lost when magnetized unidirectionally. Then, the multidirectional magnetization method is proposed to fuse the images detected under different magnetization orientations. It causes a critical problem: the existing image registration methods cannot be applied to align the images because the images are different when detected under different magnetization orientations. This study presents a novel image registration method for MFL visualization to solve this problem. In order to evaluate the registration, and to fuse the information detected in different directions, the mutual information between the reference image and the MFL image calculated by the forward model is designed as a measure. Furthermore, Particle Swarm Optimization (PSO) is used to optimize the registration process. The comparative experimental results demonstrate that this method has a higher registration accuracy for the MFL images of complex cracks than the existing methods.<\/jats:p>","DOI":"10.3390\/e25010167","type":"journal-article","created":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T02:29:55Z","timestamp":1673836195000},"page":"167","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Image Registration for Visualizing Magnetic Flux Leakage Testing under Different Orientations of Magnetization"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3779-9461","authenticated-orcid":false,"given":"Shengping","family":"Li","sequence":"first","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gaofei","family":"Liu","sequence":"additional","affiliation":[{"name":"China Petroleum Pipeline Insptection Technologies Co., Ltd., Langfang 065000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nanhui","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lulu","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8906-0576","authenticated-orcid":false,"given":"Libing","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cong","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6200407","DOI":"10.1109\/TMAG.2019.2897669","article-title":"Evaluation of a Magnetic Dipole Model in a DC Magnetic Flux Leakage System","volume":"55","author":"Hosseingholizadeh","year":"2019","journal-title":"IEEE Trans. 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